Geodesic
New examples of compact cosymplectic solvmanifolds
Archivum mathematicum, Tome 34 (1998) no. 3, pp. 337-345 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we present new examples of $(2n+1)$-dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the pro\-duct of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\geq 0$ and $m+r=n.$ These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the $2n$-dimensional real torus. In the particular case $n=1,$ using the examples obtained, we conclude that a $3$-dimensional compact flat orientable Riemannian manifold with non-zero first Betti number admits a cosymplectic structure. Furthermore, if the first Betti number is equal to $1$ then such a manifold is not topologically equivalent to the global product of a compact Kähler manifold with the circle $S^1.$
In this paper we present new examples of $(2n+1)$-dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the pro\-duct of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\geq 0$ and $m+r=n.$ These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the $2n$-dimensional real torus. In the particular case $n=1,$ using the examples obtained, we conclude that a $3$-dimensional compact flat orientable Riemannian manifold with non-zero first Betti number admits a cosymplectic structure. Furthermore, if the first Betti number is equal to $1$ then such a manifold is not topologically equivalent to the global product of a compact Kähler manifold with the circle $S^1.$
Classification : 53C15, 53C55, 53D35
Keywords: cosymplectic manifolds; solvmanifolds; Kähler manifolds; suspensions; flat Riemannian manifolds 
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     author = {Marrero, J. C. and Padron, E.},
     title = {New examples of compact cosymplectic solvmanifolds},
     journal = {Archivum mathematicum},
     pages = {337--345},
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     zbl = {0968.53054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a1/}
}
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Marrero, J. C.; Padron, E. New examples of compact cosymplectic solvmanifolds. Archivum mathematicum, Tome 34 (1998) no. 3, pp. 337-345. http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a1/

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